Taking orders

: : : What does the phrase "Of the order of" mean?
: : If you mean "on the order of," it means similar to, or as an example of.
: : SR

: I would agree, and say that "order" in this case refers to "order of magnitude," so that something is similar, specifically similar in size and scope.

'Of the order of' is an indication of size. I suspect it may be a technical term that has taken on a popular but less exact meaning. I would understand an increase of the order of five to be a fivefold increase. Is there a mathematician in the house?
Order - Mathematics - The sum of the exponents to which the variables in a term are raised; degree.

'On the order of' is not a phrase that I've ever encountered before. It's certainly not commonly used in England. Here's a definition from the internet, both examples seem to be American;
a. Of a kind or fashion similar to; like: a house on the order of a mountain lodge.
b. Approximately; about: equipment costing on the order of a million dollars.